JP2017151050A - Calibration method, program, measurement device, and product manufacturing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calibration method that is advantageous to improvement in measurement errors.SOLUTION: A calibration method measuring a distance to an object according to a principle of triangulation is configured to obtain an amount of change in baseline length, and an amount of change in angle so that a value of an objective function using the amount of change in baseline length and the amount of change in angle as a variable and set about a location of an image of a calibration reference satisfies an allowable condition under a limitation condition set to one, selected on the basis of a measurement error of the distance about the calibration reference, of an amount of change in baseline length between one optical system and other optical system and an amount of change in angle formed with an optical axis of the one optical system and an optical axis of the other optical system.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a calibration method, a program, a measuring device, and an article manufacturing method.

  As a method for measuring the shape of an object in a non-contact manner using light, a measuring device using the principle of triangulation is known. As this measuring apparatus, for example, there is an apparatus including a projection unit that projects pattern light onto an object and an imaging unit that images the object. In this case, the shape of the object is obtained using information on the relative position and orientation of the projection unit and the imaging unit acquired in advance. The measurement accuracy is adjusted by adjusting the relative distance and posture between the projection unit and the imaging unit. As a method for adjusting the measurement accuracy, there is a method of obtaining a reprojection error of a measurement apparatus and adjusting a positional relationship between a projection unit and an imaging unit so that the reprojection error is minimized (Patent Document 1).

Japanese Patent Laying-Open No. 2015-106287

  However, for example, when the measurement error amount in the object mounting surface has anisotropy in the surface (depending on the direction), the measurement error may be reduced even if the reprojection error is minimized by the method of Patent Document 1. It may not improve.

  An object of the present invention is, for example, to provide a calibration method for a measurement apparatus that is advantageous for improving measurement errors.

  In order to solve the above problems, the present invention is a calibration method of a measuring apparatus that measures the distance to an object based on the principle of triangulation, and changes in the baseline length between one optical system and another optical system. And the amount of change in the angle between the optical axis of one optical system and the optical axis of the other optical system, and the constraint condition set for one selected based on the distance measurement error with respect to the calibration standard. Below, the amount of change in the baseline length and the change in the angle so that the value of the objective function set with respect to the position of the image of the calibration reference, with the amount of change in the baseline length and the amount of change in the angle as variables, satisfies the allowable condition. It is characterized by obtaining an amount.

  ADVANTAGE OF THE INVENTION According to this invention, the calibration method of the measuring device advantageous for the improvement of a measurement error can be provided, for example.

It is a figure which shows the positional relationship of the object for calibration at the time of performing the calibration method of the measuring device which concerns on 1st Embodiment, and a measuring device. It is a flowchart which shows the calibration method which concerns on 1st Embodiment. It is a flowchart explaining the determination method of the allowable range of adjustment amount. It is a flowchart which shows the calibration method which concerns on 2nd Embodiment. It is a figure which shows the anisotropy of the flowchart and the measurement error which show the calibration method which concerns on 3rd Embodiment. It is a figure which shows the calibration apparatus which performs the calibration method which concerns on 1st Embodiment thru | or 3rd Embodiment, and a measuring device.

  Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings.

(First embodiment)
FIG. 1 is a diagram illustrating a positional relationship between a calibration object and a measurement device when the measurement device calibration method according to the present embodiment is executed. The measurement apparatus 100 according to the present embodiment includes two optical units 110 and 120. Either one of the optical units 110 and 120 may be a projection optical unit that projects pattern light, or both may be imaging units that image an object. For example, in the case where one is a projection optical unit, it is possible to obtain a reprojection error using information of a pattern of projection light, and to adjust the measurement apparatus using the obtained reprojection error. The number of optical units is not limited to two and may be more than two. A line connecting the optical center 111 of the optical unit 110 and the optical center 121 of the optical unit 120 is a base line 140. In the present embodiment, the angle formed by the optical axis of the optical unit 110 and the optical axis of the optical unit 120 is expressed as the postures of the two optical units. An object can be measured using the principle of triangulation from the length of the base line 140 (base line length) and the attitudes of the two optical units. Here, the optical center represents the pupil position on the object side of the optical system of the optical unit. Here, an X axis and a Y axis orthogonal to each other are taken in a plane on which the object is placed, and a Z axis is taken in a direction orthogonal to the XY plane.

  The measurement error and the reprojection error are obtained using calibration standards (calibration objects) 151 and 152. The calibration references 151 and 152 have known coordinate positions, and are arranged at an interval in the Z-axis direction (direction perpendicular to the object placement surface) with respect to the measurement apparatus 100. The measurement results of the calibration standards 151 and 152 by the measuring device 100 are a measurement position 161 and a measurement position 162, respectively. A difference between the position of the calibration reference 151 and the measurement position 161 is a measurement error. Among them, measurement errors 171 and 172 indicate errors in the Z-axis direction.

  In addition, the re-projection error is obtained by calculating the projection position of the measurement position on the surface (light-receiving surface, etc.) of each optical unit obtained when each calibration reference is imaged and the coordinate position of each known calibration reference by performing a perspective projection calculation. It is obtained by calculating separation (error) from the calculated position projected on the sensor. When one of the optical units 110 and 120 is a projection optical unit, the reprojection error indicates a deviation in position on the pattern generation surface for generating a projection pattern. Adjustment of the measurement apparatus is performed so as to minimize the measurement error, but the calculation load for calculating the adjustment amount of the base line length and the posture (angle) for that purpose is generally excessive. Therefore, an adjustment is performed so that the reprojection error satisfies the allowable condition (for example, minimization).

  FIG. 2 is a flowchart showing a calibration method of the measuring apparatus according to the present embodiment. Each process is executed by a control unit and a calculation unit (both not shown) included in the measurement apparatus 100. Or it is performed by the adjustment apparatus which can communicate with a measuring device. In step S010, the measuring apparatus 100 measures the positions of the calibration references 151 and 152. The length (baseline length) and posture (angle) of the baseline 140 used for measurement are values (initial values) stored in advance by the measurement apparatus 100. In step S020, it is determined which of the baseline length and the posture is to be subject to adjustment amount limitation. In step S030, the adjustment amount is determined. In step S040, the baseline length and the posture adjustment amount are output. The output destination is a drive unit (not shown) that drives the optical unit 110 and the optical unit 120, a storage unit (calculation unit) that can communicate with the drive unit, and the like.

  Adjustment of the accuracy of the measuring apparatus is performed by adjusting the base line length or the posture so as to minimize the reprojection error, but it is not known which adjustment has a larger influence on the actual error reduction. For example, if the correlation between the adjustment amount of the baseline length and the reduction amount of the error is small, it is necessary to adjust the corner. Further, when the adjustment amount of the adjustment target with a small correlation is increased, the error may be increased. Therefore, in step S020, a target for limiting the adjustment amount is determined.

  Step S020 includes step S021 and step S022. In step S021, measurement errors 171 and 172 are calculated. In step S022, an adjustment target whose adjustment amount is limited is determined based on the calculation result.

  Step S030 includes steps S031 to S034. In step S031, an optimization problem is set in which the reprojection error satisfies an allowable condition (becomes minimized). In step S032, a constraint condition for the optimization problem is set. In steps S033 and S034, the optimization problem is adjusted by the optimization problem. A quantity is calculated.

  Here, it is desirable to set the limit of the adjustment amount of the baseline length at a relative position in the baseline 140 direction. In addition, it is desirable to set the limit of the angle adjustment amount in a plane including the base line 140. Further, the adjustment amount is not limited to the base line length and corner, but may include the position and orientation of the measuring apparatus 100 itself. The value is proportional to the base line length and corner adjustment amount, the focal length of the optical unit, May include adjustment amounts relating to optical parameters such as correction and aberration.

  The adjustment target to be limited in step S022 is determined based on the relationship between the measurement error 171 and the calibration reference 151 (or the relationship between the measurement error 172 and the calibration reference 152) when the baseline length or the angle is changed. Is called. Assuming that the optical center 111 is the origin, for example, the error dz in the Z-axis direction when the base line length changes from B to B + dB is as follows when the distance in the Z-axis direction between the measuring device 100 and the calibration reference 151 is z. It is expressed as equation (1).

  Similarly, dz when the angle changes from θ to θ + dη is expressed by the following equation (2) using the distance x in the X-axis direction in addition to the above parameters.

  As in the above formula, the correlation between the change in the baseline length and the error in the Z-axis direction (formula (1)), the correlation between the change in the angle and the error in the Z-axis direction (formula (2)), By utilizing this, it is possible to determine which one of the change in the baseline length and the change in the angle is more affected by the occurrence of the measurement error. In other words, two or more calibration standards having different distances in the Z-axis direction are measured, and the measurement result is compared with dz obtained by Equation (1) and Equation (2). Can be determined to be a factor that is greatly influenced by the occurrence of measurement errors. As a specific comparison method of the correlation degree, for example, there is a method of performing function fitting on the error dz using the equations (1) and (2) and comparing the amount of the fitting residual. Further, the present invention is not limited to this, and various methods for investigating the presence or absence of a generally known correlation degree can be applied. The factor with the lower degree of correlation (adjustment target) is the factor that limits the amount of adjustment.

  Note that the number of calibration standards is not limited to two, and a plurality of calibration standards may be arranged. It is sufficient that the calibration standard has a different distance in the Z-axis direction, and the larger the number, the more accurately the correlation can be obtained. Even if there is only one calibration reference, for example, a method may be used in which one calibration reference is attached to the drive device and driven to a plurality of positions, and information on the drive position of the drive device is used as the calibration reference coordinate position. .

  Further, the formulation according to the above formulas (1) and (2) is an example and is not limited to this. For example, it may be modified according to how to set the XYZ coordinate axes or the coordinate origin, and since Equation (2) is a complex equation, it may be simplified by approximation and replaced with the approximate equation. In other words, the target for limiting the adjustment amount can be determined based on the error dZ (depth error) information obtained from two or more calibration standards.

  In step S030, the adjustment amount is determined. FIG. 3A and FIG. 3B are flowcharts illustrating details of the determination method. As shown in FIG. 3A, in step S031, the reprojection error function with the adjustment amount as a variable is used as an objective function, and the reprojection error satisfies an allowable condition (for example, minimizes). Set. The solution to the optimization problem can be selected according to the required calculation accuracy and calculation load, and the least square method, Lagrange's undetermined multiplier method, substitution method, and the like can be selected.

  In step S032, a constraint condition for the set optimization problem is defined. Here, the constraint condition is a range of an adjustment amount that is allowed for the measurement error to satisfy the allowable condition. The allowable range is desirably determined based on an adjustment amount corresponding to the maximum value of a measurement error that can occur due to changes over time in the design of the apparatus. In addition, an error may remain even when the reprojection error is minimized. This error becomes smaller as the adjustment amount is smaller. Therefore, it is desirable to determine the allowable range of the adjustment amount in consideration of the balance between reducing the error due to the change over time and reducing the error remaining by minimizing the reprojection error. The user can appropriately determine which specific gravity is to be increased. Note that the method for determining the allowable range of the adjustment amount can be variously changed according to the risk design with respect to the change over time of the measuring device, and is not limited to one method. Further, the allowable adjustment amount may be a fixed value.

  In step S033, the optimization problem is solved under the constraint conditions defined in step S032, and the adjustment amount is calculated. On the other hand, in step S034, the optimization problem is solved without constraint conditions, and the adjustment amount is calculated.

  FIG. 3B is different in that step S032 of FIG. 3A is set to step S035. In step S035, an optimization problem for minimizing the adjustment amount is set using the function of the adjustment amount (the adjustment amount of the target determined in step S022) with the error as a variable as an objective function. When setting the objective function in step S031 and step S035, the range of the adjustment amount can be set by defining the weighting between minimizing the reprojection error and minimizing the adjustment amount. In step S033, the adjustment amount is calculated by solving the two set optimization problems. Based on the adjustment amount output in step S040, the measurement device is adjusted, and the measurement accuracy is improved.

  According to the calibration method as described above, it is possible to improve the measurement error of the measuring device by specifying the reprojection error as a calibration value and specifying the restriction target of the adjustment amount and minimizing the calibration value. As described above, according to the present embodiment, it is possible to provide a calibration method for a measurement apparatus that is advantageous for improving measurement errors.

(Second Embodiment)
FIG. 4 is a flowchart showing a calibration method of the measuring apparatus according to this embodiment. In the present embodiment, the calibration method of the first embodiment and the calibration method that does not impose restrictions as in the first embodiment are used in combination. According to the method of the present embodiment, it is possible to cope with unexpected changes such as loosening of fixing screws of members of the measuring device 100. If an unexpected change occurs, the error may not be sufficiently suppressed with a limited calibration amount. In the present embodiment, the method includes a step of determining which one of the calibration method in the case where the restriction is imposed and the calibration method in which the restriction is not employed is adopted as the calibration method.

  In the flowchart of FIG. 4, steps similar to those in the first embodiment are denoted by the same reference numerals, and description thereof is omitted. In step S050, the set of adjustment amounts obtained by the calibration method of the first embodiment is stored as a temporary adjustment amount (first adjustment amount) in a storage unit (not shown) in the measurement apparatus 100. Note that the storage unit may be provided in an apparatus (such as an adjustment apparatus that executes the calibration method) different from the measurement apparatus 100.

  In parallel with the steps S020 to S050, in step S051, a temporary adjustment amount (second adjustment amount) is obtained by solving the optimization problem set in the same manner as in step S031. At this time, no restriction is imposed as in the first embodiment. The obtained value is stored in the storage unit (step S052). In step S053, the residual error when calibration is performed with the first adjustment amount is compared with the residual error when calibration is performed with the second adjustment amount. Each residual may be calculated in steps S033 and S034 and step S051, respectively, and stored together with each adjustment amount in steps S050 and S052. In this case, in step S053, each stored residual is read from the storage unit and compared. In step S054, the adjustment amount with the smaller residual is output.

  In addition, although the example which acquires 1st adjustment amount and 2nd adjustment amount in parallel was shown above, it is not limited to this, depending on the arithmetic processing performance of the calibration apparatus which implements the calibration method of this embodiment, both It is also possible to perform the methods in order. In this case, the order in which both are obtained does not matter. Further, the residual to be compared may be a residual in a specific direction. For example, a user who places importance on errors in the XY plane may compare residuals in the XY plane, and a user who places importance on errors in the Z-axis direction may compare residuals in the Z-axis direction.

  According to the adjustment method of the present embodiment, it is possible to improve the measurement error even when an abnormal change that does not meet the design assumption such as loosening of the fixing screw of the measuring device 100 occurs, and the calibration method is The same effect as the first embodiment is achieved.

(Third embodiment)
FIG. 5A and FIG. 5B are a flowchart illustrating the calibration method of the measuring apparatus according to the present embodiment and a diagram illustrating the anisotropy of the measurement error. In the present embodiment, it is determined whether or not it is necessary to limit the adjustment target before the execution of step S22. This determination is made based on the presence or absence of measurement error anisotropy in the XY plane.

  FIG. 5A is a flowchart showing a calibration method of the measuring apparatus according to this embodiment. The same steps as those in the first embodiment are denoted by the same reference numerals, and description thereof is omitted. In step S061, the error component in the X direction and the error component in the Y direction of the measurement error acquired in the previous process are calculated, and it is determined whether the calculated error component is equal to or less than a preset threshold value. If it is equal to or less than the threshold (YES), step S051 is performed, and the adjustment amount is output in step S062. When deviating from the threshold (NO), step S022 and subsequent steps of the first embodiment are performed. Through the above steps, it is not necessary to obtain two provisional adjustment amounts as in the second embodiment, and the calibration value can be obtained in a shorter time.

  FIG. 5B is a diagram for explaining the anisotropy of the measurement error. Calibration standards 153 and 154 having different positions in the X-axis direction, calibration standards 153 having different positions in the Y-axis direction 155, and calibration standards 154 having different positions in the Y-axis direction are measured. The measurement results corresponding to the calibration standards 153 to 156 are the measurement positions 163 to 166.

  The distance in the X-axis direction between each calibration reference is indicated by a distance 180, and the distance in the X-axis direction of the measurement result is indicated by a distance 181. Here, the distance 180 may be a distance between the calibration standards 153 and 154, may be a distance between the calibration standards 155 and 156, or may be an average value thereof. The distance 181 only needs to correspond to the calculation method of the distance 180. Similarly, in the Y-axis direction, the distance in the Y-axis direction between the calibration references is indicated by a distance 182, and the distance in the Y-axis direction of the measurement result is indicated by a distance 183.

  The anisotropy of the measurement error is a value obtained by dividing the difference between the distance 180 and the distance 181 by the distance 180 (error magnification in the X-axis direction) and a value obtained by dividing the difference between the distance 182 and the distance 183 by the distance 182 (Y (Error magnification in the axial direction). That is, if the error magnification in the X-axis direction and the error magnification in the Y-axis direction are the same value, there is no anisotropy in the measurement error, and if both values are different, it is determined that the measurement error has anisotropy. In step S061, the magnitude of this anisotropy is compared with a threshold value. The magnitude of anisotropy is the difference between them or the ratio between the two.

  Depending on the magnitude of the anisotropy, the measurement error can be minimized by minimizing the reprojection error without adding a limit value to the adjustment target. Therefore, the magnitude of anisotropy determined by the user that the measurement error can be sufficiently improved without adding a limit value is set as the threshold value.

  Although FIG. 5B shows an example in which four calibration standards are used, the present invention is not limited to this. At least the error magnification in the X-axis direction and the error magnification in the Y-axis direction, or an indirect amount instead of these. Any number can be calculated. For example, two calibration standards having different X-coordinate positions and Y-coordinate positions may be used, or the accuracy may be improved by preparing a large number of calibration standards. Further, the magnification component in the X-axis direction and the magnification component in the Y-axis direction are not limited to the above definitions, and any amount that can determine whether isotropic expansion or contraction is anisotropic is acceptable. For example, the error between the calibration reference coordinate value and the measurement position may be divided by the calibration reference coordinate value. Further, the difference amount is not limited to the above definition, and any difference index may be used as long as the difference can be quantified. In other words, it is possible to determine whether to perform the adjustment with or without the restriction based on the information of the lateral error obtained from two or more calibration standards. .

  According to the calibration method of the present embodiment, the adjustment amount can be calculated in a shorter time, and the calibration method has the same effect as that of the first embodiment.

(Fourth embodiment)
FIG. 6 is a diagram illustrating a calibration apparatus 200 and a measurement apparatus 100 that execute the calibration method according to the embodiment. The calibration device 200 stores a program that causes a computer (not shown) to execute the calibration method according to the embodiment. The adjustment amount is output to a drive unit of the measurement apparatus 100, a storage unit that communicates with the drive unit, and the like. The adjustment instruction may be given by the user or by a self-determination program (not shown) or may be given at a preprogrammed periodic timing. The calibration device 200 and the measurement device 100 may be integrated, and a processing unit or the like in the measurement device may also serve as the calibration device. As described above, according to the present embodiment, it is possible to provide a calibration device that is advantageous for adjusting the accuracy of the measurement device.

(Embodiment related to article manufacturing method)
The measurement device whose accuracy is adjusted by the calibration method or the calibration device according to the embodiment described above or the measurement device including the processing unit that executes the calibration method can be used for the article manufacturing method. The article manufacturing method may include a step of measuring a distance to an object using the measuring device and a step of processing the object measured in the step. The process can include, for example, at least one of processing, cutting, conveyance, assembly (assembly), inspection, and selection. The article manufacturing method of the present embodiment is advantageous in at least one of the performance, quality, productivity, and production cost of the article as compared with the conventional method.

(Other embodiments)
In step S022 of the above embodiment, if the accuracy of specifying the adjustment amount restriction target is poor, the adjustment amount restriction target can also be specified by performing the following steps. First, the adjustment amount is calculated by limiting the corner to a preset value. In parallel with this, the adjustment amount is calculated by limiting the baseline length to a preset value. Further, the adjustment amount is calculated without limiting the corner and the base line length. Then, the same process as step S053 and step S054 is performed with the three values, and the adjustment amount with the smallest residual is output. In these processes, since the adjustment amount is calculated with brute force as to whether or not the restriction is necessary, it is not necessary to designate the restriction target. Although it takes time to calculate the adjustment amount, it is useful when the accuracy of specifying the restriction target of the adjustment amount in step S022 is poor due to the influence of noise or the like. After calculating the three values, the calculated value is compared with the adjustment amount of the constraint object obtained in advance, and the adjustment amount of the adjustment object that deviates from the previously obtained value is fixed to the value obtained in advance. A method of calculating the adjustment amount is also conceivable.

  Furthermore, if it is known from the design value information of the measuring device that the baseline length and angle are more likely to change over time, or if the amount of error caused by the change over time is known to be larger, there are restrictions beforehand. A method of determining the target can also be considered. For example, when the amount of error generated due to a change with time is larger at the corner, the baseline length is stored as a restriction target. Then, the adjustment amount is calculated without any restrictions, and if the baseline length deviates from the previously stored limit value, the adjustment amount is calculated again after fixing the baseline length to the limit value. A method of determining

  As mentioned above, although preferable embodiment of this invention was described, this invention is not limited to these embodiment, A various deformation | transformation and change are possible within the range of the summary.

100 Measuring device 110, 120 Optical unit 140 Base line

Claims (10)

A calibration method for a measuring device that measures the distance to an object based on the principle of triangulation,
Calibration standard among the amount of change in baseline length between one optical system and another optical system and the amount of change in angle between the optical axis of the one optical system and the optical axis of the other optical system Under the constraints set for one selected based on the measurement error of the distance with respect to
The objective function value set with respect to the position of the image of the calibration reference, with the change amount of the baseline length and the change amount of the corner as variables, satisfies an allowable condition.
Obtaining a change amount of the baseline length and a change amount of the angle;
A calibration method characterized by that.   The said one is selected based on the correlation of the variation | change_quantity of the said base line length, and the said measurement error, and the correlation of the variation | change_quantity of the said angle, and the said measurement error, The said one is selected. Calibration method.   The calibration method according to claim 1, wherein the measurement error relates to a plurality of different distances.   4. The calibration method according to claim 1, wherein the change amount of the baseline length and the change amount of the corner are obtained by solving an optimization problem related to the objective function. 5.   5. The objective function according to claim 1, wherein the objective function includes at least one of a term proportional to the amount of change in the baseline length and a term proportional to the amount of change in the angle, in addition to the term relating to the position. The calibration method according to any one of the above.   Of the measurement error obtained when the constraint condition is imposed on the change amount of the baseline length and the measurement error obtained when the constraint condition is imposed on the change amount of the corner, the baseline length In order to obtain a measurement error with a larger deviation from the measurement error obtained when no constraint condition is imposed on either the change amount or the change amount of the angle, the change amount of the one with the constraint condition is obtained. The calibration method according to any one of claims 1 to 5, wherein the calibration method is selected.   The calibration method according to claim 1, wherein the one is selected based on anisotropy of a magnification component of the measurement error.   A program that causes a computer to execute the calibration method according to any one of claims 1 to 7. A measuring device having a processing unit and measuring the distance to an object by the processing unit according to the principle of triangulation,
The processor is
Of the amount of change in the baseline length between one optical system and the other optical system and the amount of change in the angle between the optical axis of the one optical system and the optical axis of the other optical system, Under the constraints set for one selected based on the distance measurement error,
The objective function value set with respect to the position of the image of the calibration reference, with the change amount of the baseline length and the change amount of the corner as variables, satisfies an allowable condition.
Obtaining a change amount of the baseline length and a change amount of the angle;
A measuring device characterized by that. A step of measuring a distance to an object using the measuring device calibrated by the calibration method according to any one of claims 1 to 7 or the measuring device according to claim 9;
Processing the object subjected to the measurement in the step;
A method for producing an article comprising:

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